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Networks of $$\cdot /G/\infty $$ · / G / ∞ queues with shot-noise-driven arrival intensities

Author

Listed:
  • D. T. Koops

    (University of Amsterdam)

  • O. J. Boxma

    (Eindhoven University of Technology)

  • M. R. H. Mandjes

    (University of Amsterdam)

Abstract

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by a shot-noise process. A shot-noise rate emerges naturally in cases where the arrival rate tends to exhibit sudden increases (or shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable to analysis. In particular, we perform transient analysis on the number of jobs in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of jobs in the system by using a linear scaling of the shot intensity. First we focus on a one-dimensional setting in which there is a single infinite-server queue, which we then extend to a network setting.

Suggested Citation

  • D. T. Koops & O. J. Boxma & M. R. H. Mandjes, 2017. "Networks of $$\cdot /G/\infty $$ · / G / ∞ queues with shot-noise-driven arrival intensities," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 301-325, August.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:3:d:10.1007_s11134-017-9520-7
    DOI: 10.1007/s11134-017-9520-7
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    References listed on IDEAS

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    1. D. Anderson & J. Blom & M. Mandjes & H. Thorsdottir & K. Turck, 2016. "A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 153-168, March.
    2. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
    3. Centanni, Silvia & Minozzo, Marco, 2006. "A Monte Carlo Approach to Filtering for a Class of Marked Doubly Stochastic Poisson Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1582-1597, December.
    4. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
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